Question

If in the following figure, height of object is $H_1=+2.5cm,$ then height of image $H_2$ formed is

• A. -5 cm
• B. +5 cm
• C. +7.5 cm
• D. -7.5cm

Answer 1

Answer: (A)

Magnification is ratio of size of image to that of object.
Here, $u=-1.5f,f=-f$
From concave mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ we have,
$\frac{1}{(-f)}=\frac{1}{v}+\frac{1}{(-1.5f)}$
$\therefore \frac{1}{v}=-\frac{1}{3f}$
or $v=-3f$
Now, magnification in mirror is given by
$m=\frac{I}{O}=\frac{v}{-u}$
where $I$ is size of image, and $0$ is size of object.
Here, $O=+2.5cm$
$\therefore \frac{I}{2.5}=\frac{-3f}{-(1.5f)}$
$\therefore I=-5cm$
In case of a concave mirror, magnification may be positive or negative, but in case of convex mirror magnification is positive only.